Dooku's New Order
This is an idea that I had to write out thanks to the youtuber The Stupendous Wave's video, about what jedi thought Dooku was doing after he left the order.
Dooku never joins the Sith, but instead creates his own force based order.
Whether or not he joins the Separatists or Republic is author's decision. He could also join neither.
He is obviously the Grandmaster of this new order.
As far as his order's masters and students go, to make it more fun, recruit OCs from reviewers to either be Masters or Apprentices. The story doesn't have to revolve around them, but it just adds to the fun. Other jedi and their apprentices might also join him.
The story might also follow his first student of the new order, or one that is a couple generations down the line.
His new order's tenants are up to the author. Apparently he was going to follow a similar code that the jedi follow, but not as devout. Guessing this involves the whole attachment thing but who knows? Speaking of which.
His order would likely allow attachments. But he would teach them to temper such bonds and not let them cloud their judgment.
Dooku places a heavy emphasis on saber to saber combat. Something that the jedi weren't use to during the time the sith were in hiding. This does not mean that he puts it squarely above the other areas of training, just that one should always be ready just in case. The other areas of non-force and saber training are likely tactics, politics, governance, etc.
At the time of Episode 3, Dooku's fate is up to the author, but it should affect how his order will react.
Most importantly: Have fun.